The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
CMU Core Model Seminar
Time: Tuesday, 12 March, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET)
Speaker: Nam Trang, University of North Texas
Title: Ideals and Strong Axioms of Determinacy
Abstract: We present the main ideas behind the proof of the equiconsistency of the theories:
(1) ZF + AD_R + \Theta is regular.
(2) ZFC + CH + there is an \omega_1-dense ideal on \omega_1.
(3) ZFC + the nonstationary ideal on P_{\omega_1}(R) is strong and pseudo-homogeneous.
This resolves a long-standing open problem asked by W.H. Woodin in the 1990’s. In the first talk, we discuss some history related to this problem and the general program in descriptive inner model theory that aims to calibrate the consistency strength of theories like the above. In the next two talks, we outline some main ideas behind the proof: the forcing construction that shows (1) is an upper bound (consistency-wise) of (2) and (3), and the core model induction that shows (2), (3) are upper bounds for (1).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 12 March, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET)
Speaker: Filippo Calderoni, Rutgers University
Title: Condensation and left-orderable groups
Abstract: In this talk we will discuss the phenomenon of condensation for group actions. We will show how condensation is used to study the descriptive complexity of some countable Borel equivalence relations occurring in group theory. In particular, we will analyze the conjugacy orbit equivalence relation for the solvable Baumslag-Solitar groups on their space of left-orders. This is joint work with Adam Clay.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 13 March, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: Saharon Shelah
Title: Corrected Iteration (part 3)
Abstract: The goal will be to introduce iterated forcing posets which are homogeneous in a reasonable sense. I will start by talking about my earlier paper “Souslin Forcing” with Jaime I. Ihoda.
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 14 March, 11:30-13:00 CET
Speaker: David Schrittesser, Harbin Institute of Technology
Title: How economists forgot about multi-player utility and how we remembered
Abstract: This is all joint work with Ali M. Khan (Johns Hopkins) and Paul Arthur Pedersen (CUNY).
Game theory as practiced by economists is often couched in a setting where players pick strategies, and then a utility function tells them who has which pay off (the so-called “normal form” of a game). For two person games, an important special case is the zero sum game: the case where pay offs always sum to zero. Aumann, the sixties, defined “strictly competitive games”, two player games in which what is good for one player is bad for the other. Aumann frequently stated that this is the same class as the zero sum games—for an appropriate choice of utility function (and provided the players strategy spaces are closed under mixing).
We claim that Aumann must have known this because he knew the multidimensional theory of utility. But then in 2009, Adler, Daskalakis and Papadimitriou gave a non-trivial proof of the fact claimed by Aumann, for finite games, claiming that no such proof exists in the literature. This was generalized in 2023 by Raimondo to games where the set of strategies available to each player is an appropriate set of probability measures on [0,1] (or if you’re feeling fancy, on a standard Borel space).
In this talk, I shall show what Aumann and others must already have been aware of, but what has apparently been forgotten in the meantime: That these results, and more general ones, follow easily from the theory of mutlidimensional utility developed in the 60ies and early 70ies by Fishburn, Roberts, and others.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 14 March, 15:00 – 15:50 CET
Speaker: A. Kwiatkowska, Universität Münster
Title: Projective Fraisse limits of trees
Abstract: We continue the study of projective Fraisse limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. We focus on particular classes of epimorphisms such as monotone, confluent or simple confluent, which are adaptations to graphs of monotone or confluent maps from continuum theory. As the topological realizations of the projective Fraisse limits we obtain the dendrite D3 the Mohler-Nikiel universal dendroid, as well as new, interesting compact connected spaces (continua) for which we do not yet have topological characterizations.
The talk is based on joint work with Charatonik, Roe, Yang.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 15 March, 12.30-1.45pm New York time (18.30-20.45 CET)
Speaker: Chris Lambie-Hanson, Czech Academy of Sciences
Title: Squares, ultrafilters and forcing axioms
Abstract: A uniform ultrafilter U over a cardinal κ>ω1 is called indecomposable if, whenever λ<κ and f:κ→λ, there is a set X∈U such that f[X] is countable. Indecomposability is a natural weakening of κ-completeness and has a number of implications for, e.g., the structure of ultraproducts. In the 1980s, Sheard answered a question of Silver by proving the consistency of the existence of an inaccessible but not weakly compact cardinal carrying an indecomposable ultrafilter. Recently, however, Goldberg proved that this situation cannot hold above a strongly compact cardinal: If λ is strongly compact and κ≥λ carries an indecomposable ultrafilter, then κ is either measurable or a singular limit of countably many measurable cardinals. We prove that the same conclusion follows from the Proper Forcing Axiom, thus adding to the long list of statements first shown to hold above a strongly compact or supercompact cardinal and later shown also to follow from PFA. Time permitting, we will employ certain indexed square principles to prove that our results are sharp. This is joint work with Assaf Rinot and Jing Zhang.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 15 March, 1.30-3.00pm Toronto time (19.30-21.00 CET)
Speaker: Frank Tall, University of Toronto
Title: An undecidable extension of Morley’s theorem on the number of countable models
Abstract: Joint work with Christopher J. Eagle, Clovis Hamel, Sandra Müller.
We show that Morley’s theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, large cardinals, and Inner Model Theory.
Information: Please see the conference webpage for the login information.
European Set Theory Society 